Sounds like the low pressure cutout switch is stopping your compressor running, especially if the "5 seconds" you mention are exactly the same length each time. Not enough refrigerant would be the usual cause, but the reason for the refrigerant loss is harder to tie down - possibly a seal or a loose valve seat or even a pinhole in a copper tube. Best solution now would be to get a refrigerator mechanic to top it up and check for leaks - get a quote first to check - 'fridge gas is getting costly.
Other possible solution is that the low pressure switch itself is faulty, relatively inexpensive to replace (but unfortunately you will need at least a partial gas recharge on most types of system after) - your fridge gas guy will be able to check very easily if there is adequate gas in the system, and should check this low pressure switch if there is not.
Usually this is fixable many times, just check the cost first.
Hope this helps :)

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Difficult for you to check this I'm afraid, if the fan on the cooling unit is working unless you have an experienced 'ear' you will not hear the compressor running or worse still occasionally clicking.
Possible faults are
1. Compressor not running (the fan will run even if the compressor does not) electrical fault
2. Compressor seized (consult your service guy) also true for the rest of these
3. Compressor not pumping
4. Refrigerant leak

If the compressor is overheating I would check the condensor fan and make sure it's turning. Sounds like you wouldn't have noticed this already though. Also, if the compressor is turning on for 5 or 10 seconds and then clicking off then your start relay is probably bad. Pull the relay off the compressor and shake it. If something is loose inside then it's bad. That is, if it's a whirlpool made kenmore. Kenmore doesn't make appliances they only brand them. The refrigerator could have been made by Whirlpool, Frigidaire, GE, LG, Maytag, Amana, or other. So, it's depenant on who made it.

While moving the unit you may have jammed or budged the start capacitor which is keeping your unit from turning on. It is located in the back of the unit near the compressor it is oval shaped and silver in color with two wires running out of it. Get the number off of it, go online and search for beverage-air commercial freezer parts. You will need to have the model number to make sure that you get the right parts. Please rate

your freezer is short cycling which is bad for the compressor. Usually there is an internal overload in the compressor that automatically resets as the compressor cools. Check to see that all of the coils are clean and the small fan is blowing. this will make sure that the airflow correct. look for signs of oil around the compressor, the coils, and any connecting tubing. if you find oil, this is a sign of refrigerant leaks. the refrigerant is what cools the compressor and it wont run long in an overheated condition. it will finally fail in the open position and not come back on.(compressor overload switch) If this is the case you may replace it cheaper

First, make sure the refrigerant coils underneath the unit are not dirty. If so, clean them off.

Second, make sure the compressor (underneath the refrigerator) is running.

Third, make sure the compressor fan (underneath the refrigerator close to the compressor) is turning. This fan should always be turning when the compressor is running. It removes heat from the refrigerant coils and transfers it to the outside.

Fourth, make certain the evaporator fan (in the freezer, likely behind an access panel) is turning.

The fans are controlled with a clixon that has a cut in at 5 degrees, and cut out at 20 degrees. If the unit is running and the fans are not comng on then I would have to say you are out of freon. But your condensor fan could be running and the compressor NOT be running which could be a problem with your compressor. Find out if your compressor is running by taking an amp draw. If compressor IS running then you are low on freon. If the compressor is running and your evaporator coil is cold and your fans AREN'T coming on then your clixon is bad.

compressor is running overloaded possible problems bad relay/overload /capacitor dirty or clogged condensers if the unit uses a condenser fan suspect a bad fan. and defective thermostats are notorious for short cycling. id check the coils first and if dirty clean up maybe that can be the major problem.